I've been studying horse fencing for a while on the internet and observing what fences other horse owners in my area use. I have found that your "serious" horse owners will run a 3 rail vinyl or wooden fence. I have also observed the newer electric tape fencing Slamffire mentioned in his post, along with plain old barbed wire, woven wire with 1 barbed strand and just about every other combination already mentioned.
For most people, cost is a big factor. No-Climb fence, vinyl and wood are excellent choices for horses, but is considerably more expensive than standard woven wire. It seems like a woven wire fence with a hot top wire is an economical option and will discourage horses from pushing against the fence, or even getting too close to it after the first shock to the nose. The electric tape is also an economical choice, but seems to sag after a while.
A big consideration for me when I install our fence in the near future is predator control, primarily from my neighbors German Shepard, Lab and two little yappy dogs. I need fencing to prevent roaming canines from entering the pasture, attacking live-stock and spooking the horses, or causing someone from being thrown from a spooked horse. So far, with the encouragement of local law enforcement, the neighbor has been keeping his dog fenced, but they still get out occaisionally, like last night I observed them out running the road.
So for economics and protection from inconsiderate neighbors who don't control their dogs, I will be installing woven wire with an energized strand at the top when the time comes to install our fencing. If cost were no option, I would really like to use the No-Climb, with an 8' heavy-duty, vinyl coated chain-link between me and the inconsiderate neighbor.